標題:

數學題 (1+x)^5 = 15x

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solve x (1+x)^5 = 15x

最佳解答:

We use the Newton's method to find the approximate root as follows: Let f(x) = (1 + x)5 - 15x, then we have: f(0) = 1 and f(1) = -15 Thus, we are sure that there's a root between x = 0 and x = 1 Also f'(x) = 5(1 + x)4 - 15 Starting from x0 = 0: x1 = x0 - f(x0)/f'(x0) = 0.1 x2 = x1 - f(x1)/f'(x1) = 0.11439 x3 = x2 - f(x2)/f'(x2) = 0.11477 x4 = x3 - f(x3)/f'(x3) = 0.11477 Thus, correcting to 5 d.p., we can approximate x = 0.11477

其他解答:

(1+x)^5=15x 5+5X=15 5x=10 x=2|||||It should have 3 distinct real roots.|||||D人係咪傻o架? 好明顯就唔係 1/2 lor..|||||5+5x=15x 5=10x x=1/2|||||(1+x)^5=15x (1+x)(1+x)(1+x)(1+x)(1+x)=15x (1+2x+x^2)(1+x)(1+x)(1+x)=15x (1+3x+3x^2+x^3)(1+x)(1+x)=15x (1+4x+6x^2+4x^3+x^4)(1+x)=15x (1+5x+10x^2+10x^3+5x^4+x^5)=15x ...............Can't solve x...............|||||5+5x=15x 5=10x x=1/2(最後答案)|||||5+5x=15x 5=10x x=1/2(最後答案)
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